CHAPTER TWO
FACTORS
Specific Objectives
By the end of the topic the learner should be able to:
a.) Express composite numbers in factor form;
b.) Express composite numbers as product of prime factors;
c.) Express factors in power form.
Content
a.) Factors of composite numbers.
b.) Prime factors.
c.) Factors in power form
d.)
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Introduction Definition
A factor is a number that divides another number without a remainder.
Number Factors
12 1,2,3,4,6,12
16 1,2,4,8,16
39 1 ,3,13,39
A natural number with only two factors, one and itself is a prime
number. Or any number that only can be divided by 1 and itself. Prime
numbers have exactly 2 different factors.
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Prime Numbers up to 100.
2 3 5 7 11
13 17 19 23 29
31 37 41 43 47
53 59 61 67 71
73 79 83 89 97
Composite numbers
Any number that has more factors than just itself and 1.They can be said
to be natural number other than 1 which are not prime numbers.They
can be expressed as a product of two or more prime factors.
9=3x3
12 = 2 x 2 x 3
105 = 3 x 5 x 7
The same number can be repeated several times in some situations.
32 = 2 x 2 x 2 x 2 x 2 = 25
72 =2 x 2 x 2 x 3 x 3 = 23𝑥 32
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To express a number in terms of prime factors ,it is best to take the
numbers from the smallest and divide by each of them as many times as
possible before going to the next.
Example
Express the following numbers in terms of their prime factors
a.) 300
b.) 196
Solution
a.)
2 300
2 150
3 75
5 25
5 5
1
300 = 2 x 2 x 3 x 5 x 5
= 22𝑥 3 𝑥 52
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b.)
2 196
2 98
7 49
7 7
196 = 2 x 2 x 7 x 7
= 22 𝑥 72
Exceptions
The numbers 1 and 0 are neither prime nor composite. 1 cannot be
prime or composite because it only has one factor, itself. 0 is neither a
prime nor a composite number because it has infinite factors. All other
numbers, whether prime or composite, have a set number of factors. 0
does not follow the rules.
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End of
topic
Did you understand everything?
If not ask a teacher, friends or anybody and make sure you
understand before going to sleep!
Past KCSE Questions on the topic
1.) Express the numbers 1470 and 7056, each as a product of its prime
factors.
Hence evaluate: 14702
7056
Leaving the answer in prime factor form
2.) All prime numbers less than ten are arranged in descending order
to form a number
(a) Write down the number formed
(b) What is the total value of the second digit?
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